## Algebra 2 Common Core

Published by Prentice Hall

# Chapter 14 - Trigonometric Identities and Equations - 14-1 Trigonometric Identities - Practice and Problem-Solving Exercises: 34

#### Answer

$$\tan\theta$$

#### Work Step by Step

Simplify $$\sin^{2}\theta\csc\theta\sec\theta.$$ Use the Reciprocal Identities $$\csc\theta=\frac{1}{\sin\theta}$$ and $$\sec\theta=\frac{1}{\cos\theta}$$ to obtain $$\sin^{2}\theta\csc\theta\sec\theta=\sin^{2}\theta\bigg(\frac{1}{\sin\theta}\bigg)\bigg(\frac{1}{\cos\theta}\bigg)=\frac{\sin\theta}{\cos\theta}=\tan\theta,$$ with the last equality based on the Tangent Identity.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.